The HHL algorithm is known as an optimal[1]} in the matrix inversion task. It is also known that entanglement is a physical resource in
quantum information processing. Then, the following question arises: why maximal creation of
entanglement and complete annihilation of it do not occur? As discussed in Sec. II similar phenomenon happens in the Grover's algorithm for large \(N\) 
even though it is known to be optimal[2]} in the quantum searching task. This means that from an aspect of entanglement, both algorithms do not use
entanglement efficiently to some extent. We think there are additional quantities as well as entanglement, which may play important role in the quantum algorithm.
Similar situation happens in the quantum illumination[3]}, [4]}, [5]}. In this case the quantum discord is known to be important[6]}, [7]}.
